From supersymmetric quantum mechanics to scalar field theories

Abstract

In this work we address the reconstruction problem, investigating the construction of field theories from supersymmetric quantum mechanics. The procedure is reviewed, starting from reflectionless potentials that admit one and two bound states. We show that, although the field theory reconstructed from the potential that supports a single bound state is unique, it may break unicity in the case of two bound states. We illustrate this with an example, which leads us with two distinct field theories.

Self-gravitating kinks in two-dimensional pseudo-Riemannian universes

“…Now, let us assume that the supersymmetric factorization (38) is valid in this model and that supersymmetry is unbroken, with the superpotential W (y) being such that W (+∞) > 0 and W (−∞) < 0, as it happens in the φ 4 and sine-Gordon theories. In such a case, we can proceed backwards, i.e., we can reconstruct the kink and, to some extent, even the potential of the scalar field theory starting from the Hessian [36,37]. The reason is translational invariance, because this symmetry implies that H y has always a normalizable zero mode, the translational mode of the kink, given by f 0 = dψ K dy which, by virtue of unbroken supersymmetry, satisfies D y f 0 = 0.…”

Novel results for kinklike structures and their connections to quantum mechanics

“…This connection is an old issue and has been investigated in several works, in particular in Refs. [15][16][17][18][19][20][21][22][23][24]. Along the years, it has been shown that the subject engenders two interesting routes, one that goes from field theory to quantum mechanics, when one investigates stability of the kinklike structures in a field theory model, which leads us to a stability potential that simulates a quantum mechanical potential.…”

“…In the works [20,21] the authors presented interesting investigations concerning the reconstruction of field theories from the spectrum of quantum mechanical potentials, and these studies have motivated the recent Refs. [22][23][24] to further explore the subject, bringing novel results. For instance, in Ref.…”

Novel connection between lump-like structures and quantum mechanics

“…[1][2][3][4][5][6][7] and references therein. An interesting issue that follows from the investigation of the stability of kinks and lumps is that the linear fluctuations around them lead to the presence of potentials that may be used to describe problems in quantum mechanics [8][9][10][11][12][13][14].…”

“…The purpose of this paper is to use the deformation procedure described in [40] to extend the analysis initiated in [12][13][14] to explore new scenarios involving lumps and their relation with QM systems. The families of models considered in this work include cases that support both lump-like and kink-like configurations, potentially leading to novel applications in the various scenarios mentioned above.…”